Substrate-limited continuous culture results at 47 g/L ethanol show that the maintenance factor and the yield factor of an unstructured maintenance model are lower compared to the values at 23 g/L ethanol. Computing the results according to a structured two-compartment model predicts an enhanced turnover rate of the K-compartment (RNA fraction) by ethanol, resulting in a lower steady-state amount of K-compartment. This is in agreement with experimentally determined RNA fractions. The parameters of both models respond qualitatively in the same way to elevation of the ethanol concentration as to elevation of the temperature. In product-inhibited continuous cultures, at ethanol concentrations above 55 g/L, nearly sustained oscillations in biomass, substrate, and products were observed. The maximum ethanol concentration achieved in these continuous cultures was 70 g/L. The oscillations could be described by a structured mathematical model, in which ethanol inhibits the maximum specific growth rate indirectly by inhibiting the synthesis of an internal growth-rate-determining compound.

Zymomonas mobilis was grown in continuous cultures at 30 and 35 degrees C. The specific substrate consumption rates at 35 degrees C were higher than those at 30 degrees C. An unstructured mathematical model based on the linear equation for substrate consumption provided a statistically adequate description for cultures grown at 35 degrees C but not for cultures grown at 30 degrees C. A structured two-compartment model described growth and substrate consumption well at both temperatures. Some theoretical and practical aspects of the two-compartment model are discussed.

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson’s ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.